On multiplicity bounds for Schrodinger eigenvalues on Riemannian surfaces
Spectral Theory
2016-01-20 v2 Differential Geometry
Abstract
A classical result by Cheng in 1976, improved later by Besson and Nadirashvili, says that the multiplicities of the eigenvalues of the Schrodinger operator with a smooth potential on a compact Riemannian surface M are bounded in terms of the eigenvalue index and the genus of M. We prove that these multiplicity bounds hold for an L^p-potential, where p>1. We also discuss similar multiplicity bounds for Laplace eigenvalues on singular Riemannian surfaces.
Cite
@article{arxiv.1310.2207,
title = {On multiplicity bounds for Schrodinger eigenvalues on Riemannian surfaces},
author = {Gerasim Kokarev},
journal= {arXiv preprint arXiv:1310.2207},
year = {2016}
}
Comments
22 pages, revised version, minor stylistic corrections made, misprints corrected, to appear in Analysis & PDE